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f(x)=2x+8x^-1.For this function there are four important intervals: (-infinity,A],[A,B),(B,C), and [C,infinity) where A,B and C are either critical numbers or points at which f(x) is undefined.Find A,B and C.

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  1. f'(x) = 2 - 8/x^2
    setting this equal to zero yields x = ±2
    where y is then ±8

    I will describe the function:
    Vertical asymptote at x = 0
    Minimum point at (2,8)
    Maximum point at (-2,-8)
    Oblique asymptote y = 2x

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